Finite Group Databasebeta

← #14775797

Subgroups — #14775797

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622620C211yesmaximal, characteristic
2#13071705C211yesmaximal, characteristic, complemented
3#13069588C211yesmaximal, characteristic, complemented
4#13069382C211yesmaximal, characteristic, complemented
5#13069351C211yesmaximal, characteristic, complemented
6#13069346C211yesmaximal, characteristic, complemented
7#13069205C211yesmaximal, characteristic, complemented
8#13069184C211yesmaximal, characteristic, complemented
9#13068877C211yesmaximal, characteristic
10#13068863C211yesmaximal, characteristic
11#13068491C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic
13#13068441C211yesmaximal, characteristic
14C4×#66896C211yesmaximal, characteristic
15C11×#2349C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#385—21no—
23C11×#385—21no—
24C11×#382C2211yescharacteristic
25C11×#380—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×C11×#95—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622620C418yescomplemented
33C4⋊C4×Dic11—21no—
34#10622586—21no—
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48#10622259—21no—
49#10622259—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C22×Dic22—21no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C4×D4×C11—41no—
70C4×D4×C11C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66922—22no—
99#66922C2×C414yescomplemented
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
106#66896—22no—
107#66896C2×C414yes—
108#66896C2×C414yes—
109#66896Q814yescomplemented
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115#66872—41no—
116#66871—41no—
117#66871C2×C414yescomplemented
118#66871C2×C414yescomplemented
119C4⋊(C11⋊C8)C2×C414yescomplemented
120#66867—22no—
121#66867—41no—
122C4×C11⋊C8—41no—
123#22979—111nomaximal, Sylow
124C24×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11C22×C412yes—
129C2×D4×C11C2×Q812yes—
130C2×D4×C11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—24no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—81no—
140C22×C4×C11—81no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—24no—
155C2×Dic22—81no—
156C2×Dic22—81no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4C22×C412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C22×C412yes—
175C42×C11#4112yes—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C412yes—
183C4⋊Dic11C22×C412yes—
184C4⋊Dic11C2×Q812yes—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187C4×Dic11—42no—
188C4×Dic11—81no—
189C4×Dic11—81no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C412yes—
200C2×C11⋊C8C22×C412yes—
201C2×C11⋊C8C2×Q812yes—
202C2×#474—111no—
203#2369—111no—
204#2349D1111yescharacteristic
205#1993—111no—
206#1949—111no—
207#1943—111no—
208#1942—111no—
209#1921—111no—
210#1918—111no—
211#1864—111no—
212#1862—111no—
213#1771—111no—
214#1762—111no—
215#1762—111no—
216C4×#102—111no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11C22×D411yescharacteristic
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—22no—
228D4×C11C4×Q814yes—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—84no—
254C2×C4×C11—84no—
255C2×C4×C11—84no—
256C2×C4×C11C4×D412yes—
257C2×C4×C11C4×D412yes—
258C2×C4×C11#13712yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×Q811yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277Dic22—84no—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C11⋊C8—22no—
281C11⋊C8—41no—
282C2×C4⋊Q8—111no—
283C2×C4×D4C2×D1111yescharacteristic
284C2×C4×D4C2×D1111yescharacteristic
285C2×C4×D4C2×D1111yescharacteristic
286#474—118no—
287C2×#107—111no—
288C2×#107—111no—
289C2×#107—111no—
290C2×#106—111no—
291C2×C4⋊C8—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#97—111no—
297C2×#97—111no—
298C2×C4×C8—111no—
299#391—221no—
300#391—221no—
301#389—111no—
302#389—111no—
303#389—221no—
304#389C2×D1111yescharacteristic
305#389C2×D1111yescharacteristic
306#385—21no—
307#385—21no—
308#382C2×D1111yescharacteristic
309#380—21no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—221no—
314C4×C4⋊C4C2×D1111yescharacteristic
315C2×#95—21no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#336—111no—
325#336—111no—
326C22×C11—24no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11C2×C4×D411yescharacteristic
334C22×C11#54611yescharacteristic
335C22×C11D4×Q811yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57611yescharacteristic
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×C4×Q811yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#55211yescharacteristic
352C4×C11#55411yescharacteristic
353Dic11—42no—
354Dic11—42no—
355Dic11—42no—
356Dic11—81no—
357C22×Q8—221no—
358C22×D4C22×D1111yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C4⋊Q8—114no—
367C4⋊Q8—222no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—41no—
372C4×D4—41no—
373C4×D4C4×D1114yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22⋊D1111yescharacteristic
384C2×C4⋊C4C22⋊D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—221no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42C22×D1111yescharacteristic
395C2×C42C22×D1111yescharacteristic
396C2×C42C22×D1111yescharacteristic
397#107—114no—
398#107—114no—
399#107—441no—
400#106—441no—
401C4⋊C8—114no—
402#102—114no—
403#102—114no—
404#102—114no—
405#102—222no—
406#97—222no—
407#97—441no—
408C4×C8—441no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95C22⋊D1111yescharacteristic
419#95C22⋊D1111yescharacteristic
420C2×C11—44no—
421C2×C11#236011yescharacteristic
422C2×C11C4×#13711yescharacteristic
423C2×C11#294811yescharacteristic
424C2×C11#331411yescharacteristic
425C2×C11#331911yescharacteristic
426C2×C11#338511yescharacteristic
427C2×C11#338911yescharacteristic
428C24—21no—
429C2×Q8—224no—
430C2×Q8—881no—
431C2×Q8—881no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4C2×C4×D1112yes—
436C2×D4#434112yes—
437C2×D4Q8×D1112yes—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C23×D1111yescharacteristic
461C2×C8—112no—
462C2×C8—112no—
463C2×C8—112no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—112no—
485C4⋊C4—224no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4C2×C4×D1112yes—
494C22⋊C4—24no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—442no—
502C42—881no—
503C42—881no—
504C42C2×C4×D1112yes—
505C42#433912yes—
506C11#2297911yescharacteristic, complemented, Sylow
507C23—22no—
508C23—22no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23C22×C22⋊D1111yescharacteristic
515Q8—884no—
516D4—22no—
517D4—22no—
518D4—22no—
519D4#6694014yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—84no—
545C2×C4—84no—
546C2×C4—84no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4C4×C22⋊D1112yes—
560C2×C4C4×C22⋊D1112yes—
561C2×C4#6700412yes—
562C2×C4C22×C4×D1111yescharacteristic
563C2×C4C2×#433911yescharacteristic
564C2×C4C2×#434111yescharacteristic
565C2×C4#6703711yescharacteristic
566C2×C4C2×Q8×D1111yescharacteristic
567C2×C4#6704011yescharacteristic
568C8—222no—
569C8—222no—
570C8—222no—
571C8—441no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×C4×C22⋊D1111yescharacteristic
580C22#1062333711yescharacteristic
581C22Q8×C22⋊D1111yescharacteristic
582C22#1062335311yescharacteristic
583C22C2×#6700411yescharacteristic
584C22#1062336611yescharacteristic
585C22#1062336611yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—442no—
596C4—442no—
597C4—442no—
598C4—881no—
599C4C2×#6694011yescharacteristic
600C4#1062303511yescharacteristic
601C4#1062304211yescharacteristic
602C4#1062304411yescharacteristic
603C2—44no—
604C2#1307162111yescharacteristic
605C2C4×#6700411yescharacteristic
606C2#1307746611yescharacteristic
607C2#1308069711yescharacteristic
608C2#1308077211yescharacteristic
609C2#1308152611yescharacteristic
610C2#1308157011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2349C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2349D11
hypocenterC11#22979
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13071705C2semidirect
3. #13069588C2semidirect
4. #13069382C2semidirect
5. #13069351C2semidirect
6. #13069346C2semidirect
7. #13069205C2semidirect
8. #13069184C2semidirect
11. #13068491C2semidirect
32. #10622620C4semidirect
99. #66922C2×C4semidirect
109. #66896Q8semidirect
117. #66871C2×C4semidirect
118. #66871C2×C4semidirect
119. C4⋊(C11⋊C8)C2×C4semidirect
506. C11#22979semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226202
#130717052
#130695882
#130693822
#130693512
#130693462
#130692052
#130691842
#130688772
#130688632
#130684912
#130684412
C4×#668962
C11×#23492
#2297911